When he finished his last competitive lap Saturday, for the gold-medal winning American 4x100 medley relay, his professional to-do must have had a whole lot of check marks.

More than any other athlete at these Games, perhaps, he has “inspired a generation” – as the London Olympic motto goes. In fact, they were in the pool with him.

When 15-year-old American Katie Ledecky won the 800-meter freestyle Friday, the first memory that she recounted was of meeting Michael Phelps and how much it meant to her that before her race, he wished her good luck.

When 20-year-old South African Chad le Clos beat Mr. Phelps by 0.01 seconds in the 200-meter butterfly on Tuesday, he said: “Phelps is my hero, and I love the guy…. You don’t understand what this means to me. This is the greatest moment of my life.”

He has changed perceptions of the possible and laid a marker for the enormous work needed to achieve the extraordinary. He pushed Ryan Lochte to flip tires and pull chains in order to beat him. He inspired Missy Franklin to swim in more Olympic events in London than any other American women had before.

In short, he has done precisely what he said he intended to do: He has profoundly changed the trajectory of the sport he loves.

The other legacy: records

But his most long-lived legacy might be on the record books themselves.

America’s fickle Olympic interests could – and almost certainly will – shift again with the rise of new athletes in different sports. But until the Olympics change in some unforeseen way, the records he established might never be broken.

To a baseball fan, the number 56 is shorthand for the unbelievable and unbreakable. It is the number of consecutive games in which New York YankeeJoe DiMaggio had a hit. Since he did it 1941, no one has broken it. No one has really come close.

Now, it appears, the Olympics have their DiMaggio – three times over.

Amazingly, Phelps’s record of eight gold medals in a single Olympics could be the most “vulnerable,” for lack of a better word. Because of the Lochtes and Franklins he has inspired, it is possible someone could at least tie his eight gold medals, though London has only underscored how enormously difficult that would be.

But 22 career medals – 18 of them gold. It is hard to see how anyone will ever match those. The latter is so astounding as to be almost indecent.

Put one way, Phelps now has as many gold medals as the second most decorated Olympian of all time – Soviet gymnast Larisa Latynina – has medals.

Realistically, only a swimmer could even consider trying to match these marks. There simply aren’t enough medal opportunities in other sports.

Jesse Owens, Carl Lewis, and Marion Jones were the Phelpses of track and field, and the most they could win was four medals in any one Olympics – 100 meters, 200 meters, 4x100 relay, and long jump. They would need to win gold in each of those for five consecutive Olympic Games to top Phelps.

Chief of the London organizing committee Sebastian Coe suggested British rower Steve Redgrave might be the best Olympian ever simply because he won one gold medal in five consecutive Olympics. To suggest that a track athlete could do the same in four events strains common sense to the breaking point.

Moreover, what Ms. Latynina did in gymnastics is now almost certainly impossible – at least in women’s gymnastics. She competed in the first of her three Games at age 20 and her last at 28. Today, that seems almost comic. American Shawn Johnson, also age 20 and with four Olympic medals already to her name, tried to make her second Olympics this year and couldn’t. The same was true of Beijing Olympic medalists Nastia Liukin (22) and Alicia Sacramone (24).

So could a female gymnast not only qualify for three Olympics but win gold in every single event (team, all-around, beam, bar, floor, and vault) each time? No.

Even so, she would have only tied Phelps.

Men’s gymnastics offers a scenario more feasible, but only slightly. Men do more frequently compete in multiple Olympics, and they have more events in which they can medal (eight). So take the Russian Unified team’s Vitaly Scherbo, who won six gold medals in 1992 (team, all-around, rings, high bar, parallel bars, and vault), and mix him with Japan’s Sawao Kato, who won medals in three straight Olympics (1968, 1972, 1976), and voilà, Michael Phelps in a singlet.

Of course, Kato won only eight medals, and Scherbo competed in only one more Games, and didn’t win a single gold (though he did win four bronze medals).

At the moment, no gymnast is even near Phelps's universe. Kohei Uchimura, who some consider the greatest male gymnast all all time, is competing in only three events here – team, all-around, and floor. He won two medals in Beijing (neither gold), meaning if he stays on his current pace he can look forward to topping Phelps’s career medal count at the 2040 Olympics.

No word yet on whether Phelps is planning to attend the ceremony.

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